Practice Number System Aptitude Questions:


Overview:


Questions and Answers Type:MCQ (Multiple Choice Questions).
Main Topic:Quantitative Aptitude.
Quantitative Aptitude Sub-topic:Number System Aptitude Questions and Answers.
Number of Questions:10 Questions with Solutions.

  1. Find the LCM of 21, 28, and 32?

    1. 572
    2. 672
    3. 678
    4. 770


Answer: (b) 672

Solution:

Step(1): Factorize the numbers into their prime factors.$$ 21 = 3 \times 7 = 3^{1} \times 7^{1} $$ $$ 28 = 2 \times 2 \times 7 = 2^{2} \times 7^{1} $$ $$ 32 = 2 \times 2 \times 2 \times 2 \times 2 = 2^{5} $$ Step(2): Collect all the distinct factors with their maximum available power.$$ = 2^{5}, \ 3^{1}, \ 7^{1} $$ Step(3): Multiply the collected factors.$$ = 2^{5} \times 3^{1} \times 7^{1} $$ $$ = 32 \times 3 \times 7 = 672 $$


  1. Find the HCF of \(\frac{6}{7}\) and \(\frac{7}{8}\)?

    1. \(\frac{1}{56}\)
    2. \(\frac{1}{58}\)
    3. \(\frac{1}{62}\)
    4. \(\frac{1}{66}\)


Answer: (a) \(\frac{1}{56}\)

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)
$$ HCF = \frac{HCF \ of \ (6,7)}{LCM \ of \ (7,8)} $$ $$ = \frac{1}{56} $$

  1. Find the HCF of 15, 25, 45?

    1. 2
    2. 3
    3. 4
    4. 5


Answer: (d) 5

Solution: Step(1): Factorize the numbers into their prime factors.$$ 15 = 3 \times 5 = 3^{1} \times 5^{1} $$ $$ 25 = 5 \times 5 = 5^{2} $$ $$ 45 = 3 \times 3 \times 5 = 3^{2} \times 5^{1} $$ Step(2): Collect all the common factors with their minimum available power.$$ = 5^{1} = 5 $$ Here, 5 is the highest positive number that can divide 15, 25, and 45 exactly.


  1. Which one of the following is the LCM of \(\frac{15}{4}\), \(\frac{18}{5}\), and \(\frac{20}{7}\)?

    1. 120
    2. 150
    3. 180
    4. 220


Answer: (c) 180

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (15, 18, 20)}{HCF \ of \ (4, 5, 7)} $$ $$ = \frac{180}{1} = 180 $$

  1. Find the HCF of 120, 150, 180?

    1. 10
    2. 20
    3. 30
    4. 60


Answer: (c) 30

Solution: Step(1): Factorize the numbers into their prime factors.$$ 120 = 2 \times 2 \times 2 \times 3 \times 5 $$ $$ = 2^{3} \times 3^{1} \times 5^{1} $$ $$ 150 = 2 \times 3 \times 5 \times 5 = 2^{1} \times 3^{1} \times 5^{2} $$ $$ 180 = 2 \times 2 \times 3 \times 3 \times 5 $$ $$ = 2^{2} \times 3^{2} \times 5^{1} $$ Step(2): Collect all the common factors with their minimum available power.$$ = 2^{1}, \ 3^{1}, \ and \ 5^{1} $$ Step(3): Multiply the collected factors.$$ = 2^{1} \times 3^{1} \times 5^{1} $$ $$ = 2 \times 3 \times 5 = 30 $$ Here, 30 is the highest positive number that can divide 120, 150, and 180 exactly.


  1. Find the LCM of \(\frac{65}{20}\), \(\frac{75}{35}\), and \(\frac{80}{9}\)?

    1. 15600
    2. 15750
    3. 15820
    4. 15950


Answer: (a) 15600

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (65, 75, 80)}{HCF \ of \ (20, 35, 9)} $$ $$ = \frac{15600}{1} = 15600 $$

  1. Which of the following is the HCF of 49, 64, and 99?

    1. 1
    2. 2
    3. 3
    4. 4


Answer: (a) 1

Solution: Step(1): Factorize the numbers into their prime factors.$$ 49 = 7 \times 7 = 7^{2} $$ $$ 64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^{6} $$ $$ 99 = 3 \times 3 \times 11 = 3^{2} \times 11^{1} $$ There is no common number among the factors, so the HCF must be 1.


  1. Which one of the following is the LCM of 7, 11, 13, and 17?

    1. 1
    2. 17017
    3. 7
    4. 65


Answer: (b) 17017

Solution:

Step(1): Factorize the numbers into their prime factors.$$ 7 = 7^{1} $$ $$ 11 = 11^{1} $$ $$ 13 = 13^{1} $$ $$ 17 = 17^{1} $$Step(2): Collect all the distinct factors with their maximum available power.$$ = 7^{1}, \ 11^{1}, \ 13^{1}, \ and \ 17^{1} $$ Step(3): Multiply the collected factors.$$ = 7 \times 11 \times 13 \times 17 = 17017 $$


  1. Find the LCM of \(\frac{10}{9}\), \(\frac{12}{11}\), and 25?

    1. 2
    2. 150
    3. 300
    4. 600


Answer: (c) 300

Solution: \(LCM \ of \ fractions = \frac{LCM \ of \ Numerators}{HCF \ of \ Denominators}\) $$ LCM = \frac{LCM \ of \ (10, 12, 25)}{HCF \ of \ (9, 11, 1)} $$ $$ = \frac{300}{1} = 300 $$

  1. Find the HCF of 18, 24, and \(\frac{6}{5}\)?

    1. \(\frac{7}{5}\)
    2. \(\frac{4}{5}\)
    3. \(\frac{8}{5}\)
    4. \(\frac{6}{5}\)


Answer: (d) \(\frac{6}{5}\)

Solution: \(HCF \ of \ fractions = \frac{HCF \ of \ Numerators}{LCM \ of \ Denominators}\)
$$ HCF = \frac{HCF \ of \ (18, 24, 6)}{LCM \ of \ (1, 1, 5)} $$ $$ = \frac{6}{5} $$